n^2+2n-37=0

Solution for n^2+2n-37=0 equation:

Simplifying
n2 + 2n + -37 = 0

Reorder the terms:
-37 + 2n + n2 = 0

Solving
-37 + 2n + n2 = 0

Solving for variable 'n'.

Begin completing the square.

Move the constant term to the right:

Add '37' to each side of the equation.
-37 + 2n + 37 + n2 = 0 + 37

Reorder the terms:
-37 + 37 + 2n + n2 = 0 + 37

Combine like terms: -37 + 37 = 0
0 + 2n + n2 = 0 + 37
2n + n2 = 0 + 37

Combine like terms: 0 + 37 = 37
2n + n2 = 37

The n term is 2n.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2n + 1 + n2 = 37 + 1

Reorder the terms:
1 + 2n + n2 = 37 + 1

Combine like terms: 37 + 1 = 38
1 + 2n + n2 = 38

Factor a perfect square on the left side:
(n + 1)(n + 1) = 38

Calculate the square root of the right side: 6.164414003

Break this problem into two subproblems by setting 
(n + 1) equal to 6.164414003 and -6.164414003.

Subproblem 1
n + 1 = 6.164414003

Simplifying
n + 1 = 6.164414003

Reorder the terms:
1 + n = 6.164414003

Solving
1 + n = 6.164414003

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + n = 6.164414003 + -1

Combine like terms: 1 + -1 = 0
0 + n = 6.164414003 + -1
n = 6.164414003 + -1

Combine like terms: 6.164414003 + -1 = 5.164414003
n = 5.164414003

Simplifying
n = 5.164414003

Subproblem 2
n + 1 = -6.164414003

Simplifying
n + 1 = -6.164414003

Reorder the terms:
1 + n = -6.164414003

Solving
1 + n = -6.164414003

Solving for variable 'n'.

Move all terms containing n to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + n = -6.164414003 + -1

Combine like terms: 1 + -1 = 0
0 + n = -6.164414003 + -1
n = -6.164414003 + -1

Combine like terms: -6.164414003 + -1 = -7.164414003
n = -7.164414003

Simplifying
n = -7.164414003

Solution
The solution to the problem is based on the solutions
from the subproblems.
n = {5.164414003, -7.164414003}